Compute

First, we recall . So, we would like to rewrite the given function in a form that looks something like this. So,

Where we used that and so .

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Stumbling Robot

A Fraction of a Dot
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Evaluate the given limit

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### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

Compute

First, we recall . So, we would like to rewrite the given function in a form that looks something like this. So,

Where we used that and so .

The substitution

that you have used to evaluate the limit is not always valid and its conditions should be explicitly mentioned given the nature of the question. In general, if

, then

if at least one of the following is true: i)

in some punctured neighbourhood of or ii) is continuous at . The first condition is unsatisfied here ( is not continuous at 0) but the second one is (

in some punctured neighbourhood of 0)